Quantum Gas Microscopy of Transport in Frustrated Hubbard Systems

Ultracold atoms in optical lattices offer unique advantages for studying quantum systems. They provide a well-isolated environment in ultra-high vacuum with excellent scalability and tunability. The interaction and tunneling parameters can be precisely controlled through magnetic fields and laser intensity. Theoretical research on quantum systems faces limitations due to the exponential growth of the Hilbert space with particle number, particularly in many-body systems. Quantum gas microscopes offer a powerful alternative approach. It allows direct investigation of many-body quantum systems through single-site resolved measurements. In this thesis, we investigate two fundamental questions in many-body physics. First, we explore how geometric frustration influences the spin-spin correlation of many-body systems. The triangular lattice Hubbard model serves as a paradigmatic example of a strongly correlated, geometrically frustrated quantum system. Its rich phase diagram includes a novel spin liquid phase. We report the implementation of a site-resolved fermionic Mott insulator in a novel triangular optical lattice using lithium-6 atoms. Our system achieves temperatures below the tunneling strength, confirmed by spin-spin correlation measurements. The experimental results are analyzed using both Determinant Quantum Monte Carlo (DQMC) and Numerical Linked-Cluster Expansions (NLCE) calculations. Second, we check how interactions and disorder affect transport properties in many-body systems. We investigate the many-body localization transition in an interacting fermionic gas within a Moire lattice, formed by superimposing square and triangular lattices. By observing the equilibration of an out-of-equilibrium sample, we map the phase diagram of the interacting regime. These findings have implications for understanding localization effects in condensed matter Moire systems.